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Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator

  • Iman Ebrahimi (a1), Juan A. Carretero (a1) and Roger Boudreau (a2)

In this work, the 3-RPRR, a new kinematically redundant planar parallel manipulator with six-degrees-of-freedom, is presented. First, the manipulator is introduced and its inverse displacement problem discussed. Then, all types of singularities of the 3-RPRR manipulator are analysed and demonstrated. Thereafter, the dexterous workspace is geometrically obtained and compared with the non-redundant 3-PRR planar parallel manipulator. Finally, based on a geometrical measure of proximity to singular configurations and the condition number of the manipulators' Jacobian matrices, actuation schemes for the manipulators are obtained. Different actuation schemes for a given path are obtained and the quality of their actuation schemes are compared. It is shown that the proposed manipulator is capable of following a path while avoiding the singularities.

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1.Merlet, J.-P., Parallel Robots, 2nd ed. (Springer, Heidelberg 2006).
2.Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a planar three-degrees-of-freedom parallel manipulator,” J. Mech. Transm. Autom. Des. 110 (1), 3541 (1988).
3.Carretero, J. A., Podhorodeski, R. P., Nahon, M. A. and Gosselin, C. M., “Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator,” J. Mech. Des. 122 (1), 1724 (Mar. 2000).
4.Tsai, K. Y. and Zhou, S. R., “The optimum design of 6-DOF isotropic parallel manipulators,” J. Robot. Syst. 22 (6), 333340 (2005).
5.Hao, F. and Merlet, J.-P., “Multi-criteria optimal design of parallel manipulators based on interval analysis,” Mech. Mach. Theory 40 (2), 157171 (2005).
6.Kong, X. and Gosselin, C. M., “Type synthesis of three degree-of-freedom spherical parallel manipulators,” Int. J. Robot. Res. 23 (3), 237245 (2004).
7.Arsenault, M. and Boudreau, R., “Synthesis of planar parallel mechanisms while considering workspace, dexterity, stiffness and singularity avoidance,” J. Mech. Des. 128 (1), 6978 (2006).
8.Maciejewski, A. A. and Klein, C. A., “Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments,” Int. J. Robot. Res. 4 (3), 109117 (1985).
9.Nakamura, Y., Hanafusa, H. and Yoshikawa, T., “Task-priority based redundancy control of robot manipulators,” Int. J. Robot. Res. 6 (2), 315 (1987).
10.Lee, S. and Kim, S., “Kinematic Analysis of Generalized Parallel Manipulator Systems,” Proceedings of the IEEE Conference on Decision and Control (1993) Vol. 2, pp. 10971102.
11.Zanganeh, K. E. and Angeles, J., “Instantaneous Kinematics and Design of a Novel Redundant Parallel Manipulator,” Proceedings of the IEEE Conference on Robotics and Automation, San Diego, USA (May 1994) pp. 3043–3048.
12.Merlet, J.-P., “Redundant parallel manipulators,” Lab. Robot. Autom. 8 (1), 1724 (1996).
13.Wang, J. and Gosselin, C. M., “Kinematic analysis and design of kinematically redundant parallel mechanisms,” J. Mech. Des. 126 (1), 109118 (2004).
14.Garg, V., Nokleby, S. B. and Carretero, J. A., “Determining the Force and Moment Workspaces of Redundantly-Actuated Spatial Parallel Manipulators,” Proceedings of the 2007 ASME Design Engineering Technical Conference, Las Vegas, Nevada, USA (September 2007).
15.Ebrahimi, I., Carretero, J. A. and Boudreau, R., “3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses,” Mech. Mach. Theory 42 (8), 10071016 (2007).
16.Hassan, M. and Notash, L., “Design modification of parallel manipulators for optimum fault tolerance to joint jam,” Mech. Mach. Theory 40 (5), 559577 (2005).
17.Gosselin, C. M., Lemieux, S. and Merlet, J.-P., “A new Architecture of Planar Three-Degree-of-Freedom Parallel Manipulator,” Proceedings of the 1996 IEEE International Conference on Robotics and Automation (Cat. No. 96CH35857), Minneapolis, USA (1996) Vol. 4, pp. 37383743.
18.Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281290 (1990).
19.Merlet, J.-P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33 (1), 7–20 (1998).
20.Zanganeh, K. E. and Angeles, J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robot. Res. 16 (2), 185197 (1997).
21.Nakamura, Y., Advanced Robotics: Redundancy and Optimization. (Addison-Weslay Publishing Co., Reading, Massachusetts, USA, 1991).
22.Salisbury, J. K. and Craig, J. J., “Articulated hands: Force control and kinematic issues,” Int. J. Robot. Res. 1 (1), 417 (1982).
23.Ebrahimi, I., Carretero, J. A. and Boudreau, R., “Path Planning for the 3-PRRR Redundant Planar Parallel Manipulator,” In: Merlet, J.-P., ed., Proceedings of the 2007 IFToMM World Congress, Besançon, France, (Jun. 2007).
24.Tsai, L.-W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (Wiley-Interscience, New York, USA, 1999).
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  • ISSN: 0263-5747
  • EISSN: 1469-8668
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